No CUDA option in repository version of Blender
I've just made an install of Linux Mint 16 64bit (with the Mate window manager) and have Blender3D working with CUDA.

Here is what did:
1: After installation of Linux Mint 16 64bit I did an update (many files)
2: Reboot.
3: Enabled the proprietary Nvidia-driver
4: With the Software Manager I installed the CUDA Toolkit (nvidia-cuda-toolkit)
5: Reboot.
6: Install Blender 3D
7: In Blender 3D CUDA was now available.

I'm not sure if nr.4 and nr.6 can be switched ... but you can try.